Spin squeezing as a measure of entanglement in a two qubit system

We show that two definitions of spin squeezing extensively used in the literature [M. Kitagawa and M. Ueda, Phys. Rev. A {\bf 47}, 5138 (1993) and D.J. Wineland {\it et al.}, Phys. Rev. A {\bf 50}, 67 (1994)] give different predictions of entanglement in the two-atom Dicke system. We analyze differences between the definitions and show that the Kitagawa and Ueda's spin squeezing parameter is a better measure of entanglement than the commonly used spectroscopic spin squeezing parameter. We illustrate this relation by examining different examples of a driven two-atom Dicke system in which spin squeezing and entanglement arise dynamically. We give an explanation of the source of the difference in the prediction of entanglement using the negativity criterion for entanglement. For the examples discussed, we find that the Kitagawa and Ueda's spin squeezing parameter is the sufficient and necessary condition for entanglement.Comment: 5 pages, 4 figure

Blind encoding into qudits

We consider the problem of encoding classical information into unknown qudit states belonging to any basis, of a maximal set of mutually unbiased bases, by one party and then decoding by another party who has perfect knowledge of the basis. Working with qudits of prime dimensions, we point out a no-go theorem that forbids shift operations on arbitrary unknown states. We then provide the necessary conditions for reliable encoding/decoding.Comment: To appear in Physics Letters

Integral Transforms and PT\mathcal{PT}-symmetric Hamiltonians

The exponential Fourier transform of a given non-Hermitian $\mathcal{PT}$ -symmetric potential in the position space is Hermitian. We prove this proposition for any $\mathcal{PT}$-symmetric non-Hermitian Hamiltonians. The hermiticity of the Fourier transformed non-Hermitian Hamiltonian operator can be used as a condition for the reality of energy spectra. In the broken $\mathcal{PT}$-symmetric regime, pairs of complex eigenvalues may appear for potentials written in the position space. However, these complex pairs disappear in the momentum space and we are left only with real eigenvalues. Moreover, we comment on the holomorphic representation of non-Hermitian spin chains in which the Hamiltonian operator is written in term of analytical phase-space coordinates and their partial derivatives in the Bargmann space rather than matrices in the complex Hilbert space. Specifying to non-Hermitian $XX$ spin chain, we prove by numerically solving the quantum master equation its ability to flip from dynamical to static system by running the coupling constant from weak to strong. This would be used in building novel non-volatile memories. Finally, we test our proposition in the case of Swanson Hamiltonian.Comment: 20 pages, added section on XX spin chains and non-volatile memorie

Effect of dispersion forces on squeezing with Rydberg atoms

We report exact results concerning the effect of dipole-dipole interaction (dispersion forces) on dynamic and steady-state characteristics of squeezing in the emitted fluorescent field from two identical coherently driven two-level atoms. The atomic system is subjected to three different damping baths in particular the normal vacuum, a broad band thermal field and a broad band squeezed vacuum. The atomic model is the Dicke model, hence possible experiments are most likely to agree with theory when performed on systems of Rydberg atoms making microwave transitions. The presence of dipole-dipole interaction can enhance squeezing for realizable values of the various parameters involved

Generation of three-qubit entangled states using coupled multi-quantum dots

We discuss a mechanism for generating a maximum entangled state (GHZ) in a coupled quantum dots system, based on analytical techniques. The reliable generation of such states is crucial for implementing solid-state based quantum information schemes. The signature originates from a remarkably weak field pulse or a far off-resonance effects which could be implemented using technology that is currently being developed. The results are illustrated with an application to a specific wide-gap semiconductor quantum dots system, like Zinc Selenide (ZnSe) based quantum dots.Comment: 8 pages, 2 figure